For me, the major problem that the fieldstone method solves is that inspiration is lumpy. The inspiration faucet often doesn't just turn on when you need it to.
By collecting fieldstones (little ideas) and polishing/rewriting over time whenever one feels strongly about a particular subject, one is able to draw on an existing collection of partially-written drafts on diverse topics that can be deployed quickly. Or combine several similar ideas and deploy a more polished/comprehensive treatment of a subject than would be possible with an on-the-spot piece.
It also accounts for the fact that our interests shift. I don't know about others but I often get into phases where I become intensely interested in a subject, research it to heck until the interest peters out. I was once really interested in the topic of alleviating loneliness because I was profoundly affected by it. I'd written many fieldstones on the topic, and contemplated it a lot. If I were given a task to write about loneliness right now, I'd probably struggle because I'm no longer as intimate with (nor as interested in) the subject as I once was, but with fieldstones I can draw on all the (partial) analyses I'd done when I was in that phase.
The fieldstone method is more than just about taking notes -- it's about brewing them over time based on one's feelings.